Download 2010 Physics Final Review Packet

Physics Final Review Sheet
Energy It cannot be created or destroyed, but it can change forms. Can energy be lost? No!
Lost energy goes to the
environment. A car (system) looses energy due to air resistance, so air molecules (environment) gain energy and
move faster. Energy is conserved.
Work An object or problem has a certain amount of energy starting the problem (potential energy due to position and/or
kinetic energy due to motion). Think of work as the energy that is added (+W) to the system or subtracted (-W) from
the system. If you add a force to something that is standing still it will begin to move a distance. This requires
positive work, the product of the force used and distance moved.
W  F  d cos
Force applied over a distance. Force and distance must be parallel. Note: this does not mean
the x axis which cos usually goes along with.  is the angle between direction of motion and applied force.
K
Kinetic Energy
1 2
mv
2
Energy of moving matter. Note that doubling mass doubles kinetic energy, but doubling
velocity quadruples kinetic energy. So a car at 60mph is 4 times more lethal than 30mph.
Potential Energy
Gravitational
Spring
U  mgh
US 
Depends on height. Consider the lowest point in the problem to be zero height. This isn’t
correct, but who wants to add the radius of the earth to every number in the problem.
1 2 Energy of a compressed spring with spring constant k.
kx
2
Work Energy Theorem
Work put into a system = the change in energy of the system. If you do work on a system you add energy (+W).
W  U s
W  U
WK
W  Qheat energy
etc.
Conservation of Energy Work and work-energy theorem are great for changes in energy, when energy moves from one
thing to another or is added or subtracted. Energy cannot be created or destroyed, but can change form and be
transferred.
Internal Energyi  K i  U i  Any other energyi  Energy f  K f  U f  Any other energy f
As an example: If the problem only involves Potential Energy and Kinetic Energy
1
1
then substitute known equations mghi  mv 2 i  mgh f  mv 2 f
U i  Ki  U f  K f
2
2
The following formulas are specific short cuts usually applied when there are two extremes in the problem.
1
Gravity
A mass m starts at the highest point and ends at the lowest point, or vice versa.
mgh  mv 2
2
The big picture:
Spring
Collisions
1 2 1 2
kx  mv
2
2
If a compressed spring extends to the equilibrium position, or vice versa.
E1i  E2 i  E1 f  E2 f
Can be used by itself and with conservation of momentum below.
In collisions total energy is conserved, but kinetic energy is not unless it is completely elastic. Unlike momentum,
kinetic energy can decrease in collisions which are inelastic. But where does it go? The deformation of colliding bodies
turns into heat (internal energy). So if you take the Kinetic energy at the start, it will equal the kinetic energy at the end
plus the amount of kinetic energy dissipated. The energy dissipated is conserved: transfers to internal energy.
Power: Rate at which work is done. Powerful machines do more work in the same time, or the same work in less time.
P
W
t
P  Fv
Work or Energy delivered as a rate of time.
It involves work. Making this another very important concept. As an example you can go from energy to work to
power then to voltage and current P  IV Think Power when you see energy and time, Joules and seconds.
p  mv inertia in motion. Measure of how difficult it is to stop an object.
Momentum
Ft  p Trade off between time taken to stop and force needed to stop.
Impulse
Conservation of Momentum
Total momentum before a collision must match total momentum after. Not given
on the AP exam. One object might be standing still at the start or after.
m1v1i  m2 v2 i  m1v1 f  m2 v2 f
Completely Elastic Collision: Bounce off completely.
m1v1i  m2v 2i  (m1  m2)vf
Inelastic Collision: The objects stick together, mass adds, one velocity.
Oscillations
T
Period
1
f
Time for one revolution, measured in seconds
Frequency
The number of revolution, turns, vibrations, oscillations, rotations per second.
Spring Restoring force F   kx Displace a spring and it will return to equilibrium, center.k is the spring constant
m
Period of a spring
Depends on mass of object attached to spring and k.
Ts  2
k
Period of a Pendulum
Tp  2

g
Depends on length of the pendulum and g.
E Waves transport energy.
Energy:
Vibration / oscillation: Something must be vibrating / oscillating in order to create a wave.
Medium:
Waves must travel in a medium with one important exception.
Electromagnetic waves are the only type of wave that do not require a medium at all.
Frequency:
f Number of vibrations, oscillations, cycles, revolutions, etc. that take place each second.
Measured in Hertz (Hz) = s-1.
Period:
T  1 f Time for one complete vibration / oscillation.
Wavelength:

Velocity:
v  f  Wave velocity depends on the elasticity of the medium. Sound travels faster in metal
The length on a single wave. Measure to the same point on the next wave.
than in water and faster in water than in air. Light, however, is unusual. It is fastest in a vacuum
and slows slightly in air, and to a greater extent in water.
Amplitude:
Angular velocity
Position
Velocity
Transverse Wave:
Longitudinal Wave:
Sinusoidal:
A Maximum displacement from the equilibrium position (midline on the graph).
2 The velocity of an oscillating object in radians, substitute 180 for degrees.
T
x  A cos(t ) Shows position at a certain time A is amplitude, ω is angular velocity, t is time.
v   A sin( t ) Shows velocity at a certain time. A is amplitude, ω is angular velocity, t is time.
Particles vibrate in a direction perpendicular to the wave direction & velocity.
(also Compression, or Shock ) Particles vibrate in a direction parallel to wave direction & velocity.
When a vibrations displacement is graphed against time a sinusoidal function is plotted. It is the
graphical representation for any wave phenomenon, and looks like a transverse wave. However,
any wave, even longitudinal waves, follows the same sinusoidal pattern.

Wavelength
Amplitude
Standing wave:
Node:
When a continuous wave strikes a barrier and reflects back on itself it will create an interference
pattern (see interference below). If the phase (see phase below) of the reflected wave is exactly
opposite to the incoming wave they will superimpose creating a standing wave.
A point on a standing wave that does not move at all.
Amplitude
Wavelength
Speed depends on the mediums elasticity. When a wave travels from one medium to a different medium the speed &
wavelength change. However the frequency remains the same.
Interference: When two or more wave meet, the amplitudes add.
In phase: Waves are in phase when they have the same wavelength and the crests are aligned.
Out phase: Waves are out of phase when they the crest on one wave aligns with the trough of another.
Constructive Interference: If the waves are in phase you add them to
construct a larger amplitude.
Destructive Interference: If the waves are out phase you add them to
destroy the amplitude. The waves shown have the same amplitude and
wavelength, but any kind of wave can interfere, so different amplitudes
and wavelengths can result in many unique new wave functions.
Sound: The speed of sound in air at 25o C is 343 m/s (often rounded to 340 m/s). The speed of sound changes with
temperature since the density and elasticity of air change as temperatures fluctuate.
Pitch: Frequency
Loudness:
Amplitude
Sound waves can originate from vibrating strings or in tubes. This is the basis for musical instruments.There are two
types of tubes: those open at both ends & those closed at one end. Strings are “closed” at both ends.
Strings:
Only multiples of ½ wavelengths can fit on a vibrating string that is held fixed at each end.
node
wavelength
Open Tubes: Same as strings, multiples of ½ waves. But the waves look a little different, since the ends aren’t fixed.
Closed Tubes: Closed tubes hold multiples of ¼ waves.
1/2 wavelength
1/4 wavelength
2/2 wavelength
1/2 wavelength
More on velocity: Sound also follows the normal velocity equation v  d t . You can time the distance to lightening by
counting the seconds between the flash and the thunder. But, if you’re timing sound that makes a round trip (like an echo,
or sonar) you have to divide your final answer by 2.
Resonance: Everything has a natural vibration frequency. If you can match the natural vibration and add more wave
energy at the right frequency and wavelength you can shatter the object. Breaking a crystal glass with your voice, or the
Tacoma Narrows Bridge are examples.
Frequency :
Period:
Speed:
Velocity:
How often a repeating event happens. Measured in revolutions per second. Time is in the denominator.
The time for one revolution. T  1 Time is in the numerator. It is the inverse of frequency.
f
Traveling in circles requires speed since direction is changing.
However, you can measure instantaneous velocity for a point on the curve. Instantaneous velocity in any
type of curved motion is tangent to the curve. Tangential Velocity.
Projectile Motion
Circular Motion
Satellite Motion
The equation for speed and tangential velocity is the same v 
2 r
T
Acceleration: Centripetal Acceleration. Due to inertia objects would follow the tangential velocity. But, they don’t.
The direction is being changed toward the center of the circle, or to the foci. In other words they are
being accelerated toward the center. ac 
Force:
Centripetal Force. If an object is changing direction (accelerating) it must be doing so because a force is
acting. Remember objects follow inertia (in this case the tangential velocity) unless acted upon by an
external force. If the object is changing direction to the center of the circle or to the foci it must be forced
that way.
Gravity
v2
Centripetal means center seeking.
r
Fg  G
Fc  mac
m1m2
r2
Fc  m
and
v2
r
Fg  mg combined are mg  G
m1m2
r2
simplified is
g G
m
r2
r is not a radius, but is the distance between attracting objects measured from center to center. Is the problem asking for
the height of a satellite above earth’s surface? After you get r from the equation subtract earth’s radius. Are you given
height above the surface? Add the earth’s radius to get r and then plug this in. Think center to center.
Inverse Square Law: If r doubles (x2), invert to get ½ and then square it to get ¼. Gravity is ¼ its original value so Fg is
¼ of what it was and g is ¼ of what it was. So multiply Fg by ¼ to get the new weight, or multiply g by ¼ to get the new
acceleration of gravity. If r is cut to a (x 1/3), invert it to get 3 and square it to get 9. Multiply Fg or g by 9.
Kepler’s Three Laws of Satellite Motion
1. Satellites move in elliptical orbits. The body they orbit about is located at one of the two foci.
2. An imaginary line from the central body to the orbiting body will sweep equal areas of space in equal times.
2
3.
 T1   r1 
   
 T2   r2 
3
Compares the orbit of one satellite to another (i.e. you can use the earth’s orbit to solve for any
other planet’s orbit. Remember, in this case r is not the radius of earth, but rather the earth sun distance.
Circuits
Definition of the electric current. I avg 
Q
Electric current is defined as charge/unit time or Coulombs/second. Current is
t
usually measured in Amps (1 Amp = 1 Coulomb/second). If you are given a problem stating the flow of electrons in a conductor, you
can determine the current with this expression.
Electrical resistance of a substance. R 
sectional area of the substance and

A
Here
 represents the resistivity of the substance (ohms/meter), A is the cross-
 is the length.
Ohm’s law. V  IR The basic equation of electronics, relating voltage (electric potential) to current and resistance. Ohm’s law
allows you to solve for V, I, or R, given 2 of the 3 variables. Simple circuits can usually be solved by using Ohm’s law and the
equations for series and parallel resistors. The CURRENT through a set of resistors in SERIES is the SAME through each resistor.
The current divides up when resistors are in parallel and the total current is the sum. The VOLTAGE across a set of resistors in
PARALLEL is the SAME. The total voltage is the sum of the voltage across a set of resistors in series.
Power in an electric circuit. P  IV Remember to use the correct values for I and V when using this equation – e.g. when
determining the power dissipated by a single resistor in a larger circuit, I is the current through the resistor (not necessarily the total
current in the circuit) and V is the voltage difference across the resistor (not the total voltage of the circuit). Other useful expressions
V2
, where I is the current through the resistor and R is the resistance. Power is measured in Watts.
R
Total resistance of a group of resistors connected in series. Rs   Ri
for or P  I R
2
i
Total resistance of a group of resistors connected in parallel.
1
1

Rp
i Ri
Sample Problems:
1.
2.
3.
4.
5.
6.
A small 20 kg child falls from the branch of a tree that is 10 meters high. What is the child’s potential energy in the branch before
he falls? What is his kinetic energy just before he hits the ground? What is his kinetic energy 2 meters above the ground? What is
his speed 2 meters above the ground?
Keith, driving a 280 kg scooter at 20 km/h, smashes head on into Ruth, driving a 1000 kg truck at 15 km/h. The vehicles collide
and stick together. What speed and direction will the vehicles be just after the collision? If the vehicles had bounced off instead
of sticking together (cuz they are made of rubber or something) and Ruth’s vehicle bounced backwards at 10 km/h, what velocity
would Keith’s scooter have?
A 20 m pendulum hangs from a tall building and has an amplitude of 1.0 m. What is the period of the pendulum? What is the
angular velocity of the pendulum? What is the speed of the pendulum as it passes through the origin?
The speed of sound is 343 m/s. What is the wavelength of a tone with a frequency of 1715 Hz? What length of an open tube
would be needed for the fundamental frequency of that tone? What length of closed tube would be needed?
What is the mass of a planet with a gravitational acceleration of 2.2 m/s 2 and a diameter of 2.5x106m? How does that compare to
Earth’s mass? What velocity would an object orbiting that planet have to have if its altitude was 200,000m?
A circuit has a battery of 15V and is connected as shown.
Find the current and voltage through each resistor.